Hindawi Publishing Corporation
International Journal of Differential Equations
Volume 2013, Article ID 802324, 2 pages
http://dx.doi.org/10.1155/2013/802324
Editorial
Fractional Differential Equations 2012
Fawang Liu,1 Om P. Agrawal,2 Shaher Momani,3 Nikolai N. Leonenko,4 and Wen Chen5
1
School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, QLD 4001, Australia
Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USA
3
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
4
School of Mathematics, Cardiff University, Cardiff CF2 4YH, UK
5
Department of Engineering Mechanics, Hohai University, Xikang Road No. 1, Nanjing, Jiangsu 210098, China
2
Correspondence should be addressed to Fawang Liu; f.liu@qut.edu.au
Received 8 January 2013; Accepted 8 January 2013
Copyright © 2013 Fawang Liu et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is our pleasure to bring this third special issue of the
International Journal of Differential Equations dedicated to
Fractional Differential Equations (FDEs).
In recent years, a growing number of papers by many
authors from various fields of science and engineering deal
with dynamical systems described by fractional partial differential equations. Due to the extensive applications of FDEs
in engineering and science, research in this area has grown
significantly all around the world.
This third special issue on fractional differential equations
consists of one review article and 9 original articles covering
various aspects of FDEs and their applications written by
prominent researchers in the field.
In the paper titled as “Generalized multiparameters fractional variational calculus” by O. P. Agrawal, the author
introduces some new one-parameter GFDs, investigates their
properties, and uses them to develop several parts of FVC.
The author also shows that many of the fractional derivatives
and fractional variational formulations proposed recently
in the literature can be obtained from the GFDs and the
generalized FVC.
The papers titled as “Solving the fractional RosenauHyman equation via variational iteration method and homotopy perturbation method,” by R. Y. Molliq and M. S. M.
Noorani, titled as “Generalized monotone iterative technique
for Caputo fractional differential equation with periodic
boundary condition via initial value problem” by J. D. Ramı́rez
and A. S. Vatsala, and titled as “Solving fractional-order logistic
equation using a new iterative method” by S. Bhalekar and
V. Daftardar-Gejji introduce variational iteration and homotopy perturbation methods for solving fractional RosenauHyman, fractional differential (with periodic boundary conditions), and fractional-order logistic equations, respectively.
The paper titled as “Axisymmetric solutions to timefractional heat conduction equation in a half-space under
Robin boundary conditions,” by Y. Z. Povstenko derives
analytical solutions to time-fractional heat equation in a halfspace under Robin boundary conditions using an integral
transform technique. The paper titled as “Analytical study of
nonlinear fractional-order integrodifferential equation: revisit
Volterra’s population model” by N. A. Khan et al. proposes a
two-component homotopy method to solve Volterra’s population model.
The paper titled as “A time-space collocation spectral
approximation for a class of time fractional differential equations” by F. Huang develops a time-space collocation spectral
method for a class of time fractional differential equations.
The paper titled as “Analysis of Caputo impulsive fractional
order differential equations with applications” by L. Mahto
et al. studies the existence and uniqueness of the theorem
of Caputo impulsive fractional order differential equations
using Sadavoskii’s fixed point method. The paper titled as
“Fractional order difference equations” by J. J. Mohan and G. V.
S. R. Deekshitulu establishes a theorem on the existence and
uniqueness of solutions for various classes of fractional order
difference equations.
Finally, The paper titled as “Chaos control and synchronization in fractional-order Lorenz-like system” by S. Bhalekar
2
International Journal of Differential Equations
investigates Chaos control and synchronization in fractionalorder Lorenz-like system.
Thus, this special issue provides a wide spectrum of
current research in the area of FDEs, and we hope that experts
in this and related fields find it useful.
Fawang Liu
Om P. Agrawal
Shaher Momani
Nikolai N. Leonenko
Wen Chen
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